Question: Solve for $x$ and $y$ using elimination. ${6x-2y = 32}$ ${5x-y = 30}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-2$ ${6x-2y = 32}$ $-10x+2y = -60$ Add the top and bottom equations together. $-4x = -28$ $\dfrac{-4x}{{-4}} = \dfrac{-28}{{-4}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {6x-2y = 32}\thinspace$ to find $y$ ${6}{(7)}{ - 2y = 32}$ $42-2y = 32$ $42{-42} - 2y = 32{-42}$ $-2y = -10$ $\dfrac{-2y}{{-2}} = \dfrac{-10}{{-2}}$ ${y = 5}$ You can also plug ${x = 7}$ into $\thinspace {5x-y = 30}\thinspace$ and get the same answer for $y$ : ${5}{(7)}{ - y = 30}$ ${y = 5}$